The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.
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Symmetry class alone sets SWSSB correlation length growth to exponential (Z2, tc ~ ln L) or algebraic (U(1), tc ~ L^alpha with alpha filling-dependent) in open quantum systems, independent of spectral gap.
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Mixed-State Long-Range Entanglement from Dimensional Constraints
The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.
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Universal Dynamical Scaling of Strong-to-Weak Spontaneous Symmetry Breaking in Open Quantum Systems
Symmetry class alone sets SWSSB correlation length growth to exponential (Z2, tc ~ ln L) or algebraic (U(1), tc ~ L^alpha with alpha filling-dependent) in open quantum systems, independent of spectral gap.
- Establishing Mixed-State Phase Equivalence beyond Renormalization Fixed Points